Question: Reduce to lowest terms: $ \dfrac{2}{5} \div - \dfrac{5}{4} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{5}{4}$ is $- \dfrac{4}{5}$ Therefore: $ \dfrac{2}{5} \div - \dfrac{5}{4} = \dfrac{2}{5} \times - \dfrac{4}{5} $ $ \phantom{ \dfrac{2}{5} \times - \dfrac{4}{5}} = \dfrac{2 \times -4}{5 \times 5} $ $ \phantom{ \dfrac{2}{5} \times - \dfrac{4}{5}} = \dfrac{-8}{25} $